The overhaul of the Fire Department’s physical fitness test last year wasn’t enough for some local legislators, who began pushing a bill Monday that would require annual reviews of physical exams given by all city agencies.

“We don’t want to close the doors of opportunity simply because of unfair physical testing that has little bearing on whether applicants can do well on the job,” said City Council member Laurie Cumbo (D-Brooklyn), the bill’s sponsor, at a City Hall hearing.

“While some argue that these tests are necessary indicators of an applicant’s ability to perform job-related tasks, they actually serve to screen out a disproportionate number of women and ethnic minorities.”

Cumbo singled out the Sanitation Department’s “superman” qualifying test as biased, arguing the name “in and of itself reinforces that women need not apply.”

The bill would require the city’s little-known Equal Employment Practices Commission to hire outside experts to review the exams annually.

That was too much even for the de Blasio administration, which agreed that more has to be done to diversify some forces, but questioned whether reviews each year was “the best use of resources.”

“There are going to be policy questions that we’ll need to discuss together around what is the appropriate frequency of testing, what are the conditions that should trigger testing,” said Brittny Saunders, a deputy counsel to the mayor.

“I think these are all questions we should discuss.”

The hearing came more than a year after the FDNY revised its physical fitness requirements and lowered the bearing the functional skills test, which requires completing tasks while lugging firefighter gear, has in passing the department’s entrance exam.

But Cumbo said the low number of female firefighters — 49 out of more than 10,000 — shows the results aren’t good enough.

Representatives from the FDNY, NYPD, Corrections and Sanitation departments did not appear at the meeting, and, according, to Saunders, were not invited.